A method of reconstructing tissue elasticity while using linear perturbation is already known from the publication "Tissue Elasticity Reconstruction Using Linear Perturbation Method" by F. Kallel and M. Bertrand, IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 15, No. 3, JUNE 1996, pp. 299-313. Said publication describes a method of reconstructing the elasticity modulus of a soft tissue, which is subjected to a static external compression, on the basis of measurements of displacements caused by said compression. Said method utilizes a known algorithm for solving an inverse problem; this algorithm is called the Newton-Raphson algorithm and utilizes a direct relation which yields the image of a set of displacement fields by way of a Finite Element Model of elasticity equations and adapts said direct relation, in a least squares sense, in order to provide the distribution of the corresponding elasticity moduli. The set of axial displacement fields of tissues forms the basic data which is estimated in advance while utilizing a multi-bit correlation technique which is applied to ultrasonic signals. The problems relating to the matrix enabling the solution of the inverse problem according to the Newton-Raphson algorithm are taken into account while utilizing a known so-called Tikhonov regularization technique which utilizes the identity matrix I. A regularization technique is used so as to realize a compromise between the reliability of the data observed and the a priori information of the solution. Utilizing an echographic imaging model, said publication teaches that the algorithm converges in from 10 to 15 iterations. Figures of the cited publication show images of the elasticity modulus distribution obtained in 15 iterations by reconstruction on the basis of noisy data while utilizing the Newton-Raphson algorithm regularized for each iteration by the Tikhonov term with I.